LOSSLESS COMPRESSION OF MEDICAL IMAGE BY HIERARCHICAL SORTING

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1 OE COMPREION OF MEDICA IMAGE Y HIERARCHICA ORTING Atsush Myooym, Tsuyosh Ymmoto Grdute chool of Engneerng, Hokkdo Unversty, pporo-sh, Hokkdo, Jpn Abstrct-We propose new lossless compresson method for medcl mges, bsed on herrchcl sortng. Herrchcl sortng s technque tht cheves hgh compresson rto by detectng the regons where mge ptterns chnge bruptly, nd by sortng pxel order by vlue to ncrese predctblty. Ths method enbles control of sortng ccurcy long wth sze nd complexty. As result, we cn reduce the szes of the permutton tbles nd reuse the tbles for other mge regons. Comprson of ths method through experment revels better performnce for medcl mges generted by X-ry CT, MRI nd lrge sze CR DR nstruments. Ths technque pples qud-tree dvson method to dvde n mge nto blocks n order to support progressve decodng nd fst prevew of lrge mges. Keywords - lossless compresson, medcl mge, sortng lgorthm, herrchcl codng I. INTRODUCTION In medcl mgng, dt compresson technques re needed for rchvng the mny mges generted by medcl mgng nstruments, becuse medcl lw mndtes tht these mges be kept for long perods. In keepng wth the nture of medcl dgnoss, the orgnl mge qulty must be preserved through compresson-decompresson. Progressve retrevl s nother requrement n ths feld. It promotes fst dgnoss v rpd dt trnsmsson nd quck prevew functon. When developng medcl mge compresson, we must tke nto ccount the mge formt used n the feld. In generl, medcl mges use more bts per pxel thn stndrd photogrphs. Most medcl mges use 0- or 2-bt/pxel formts. There re two other compressble spects of medcl mges. One s tht there re extremely lrge mge formts such s for dgtl rdogrphy (DR) nd computed rdogrphy (CR). These mges re represented n pxel or hgher resolutons. The other s the cse where set of mny mges wth smlr mgng prmeters s generted. Advnced medcl mgng nstruments such s helcl-mode X-ry CT nd 3D MRI generte seres of 2D mges whose members re very smlr to ech other. Consderng these chrcterstcs, we developed new compresson lgorthm tht cheves hgh compresson performnce for medcl mges. In generl, mge compresson lgorthms consst of three steps: predcton, modelng nd encodng. Predcton s bsed on the experentl prncple tht the entropy of the predcton error s smller thn orgnl entropy f the next pxel cn be predcted frly ccurtely from the lredy coded dt []. Ths prncple s fundmentl to mge compresson. In lossless mge compresson, the lgorthms used for JPEG (lossless mode), n IO stndrd, re well known [2]. These lgorthms use severl predcton methods nd entropycodng methods dependng on the mge type. For entropycodng schemes, ether Huffmn codng or rthmetc codng s used. However, snce these compresson methods re ntended for common photogrphc mges of 8-bt/pxel formt, these re not pplcble for medcl mges n 0- to 2-bt/pxel formt. In 996, Wenberger et l. developed OCO-I (ppled to JPEG-) whch supports not only 8-bt/pxel but lso 6- bt/pxel formts [3]. OCO-I s lossless nd ner lossless compresson lgorthm whch combnes the smplcty of Huffmn codng wth the compresson potentl of smple fxed context models. nce the method employs one-pss scheme, the compresson speed s usully hgher thn tht of two-pss schemes. The compresson rto of OCO-I s better thn schemes bsed on rthmetc codng. However, OCO-I doesn't support progressve reconstructon nd t hndles only sngle mge for ech compresson process. Ths pper proposes new lossless codng method for medcl mges. To pproch the problem wth conventonl methods, we developed the new technque, herrchcl sortng. Ths method cn cheve hgh compresson rto by detectng ptterns observed n n mge set collected by X- ry CT nd MRI nstruments. Ths technque lso supports progressve decodng. II. THEORY If pxels re sorted perfectly n densty order, predctve coder genertes the smllest possble predctng code. However, tble s requred to restore the pxel postons to recover the orgnl mge. The sze of the tble s usully greter thn the sze of the orgnl mge. Herrchcl sortng does not sort the pxels n n mge ccurtely. Ths technque genertes permutton tbles nd pples those tbles to mny regons of mny herrchcl lyers. Herrchcl sortng conssts of two processes: block dvson nd permutton tble creton. In the frst process, the orgnl mge s dvded nto sub-blocks. Then, the permutton tble s creted to sort the pxels n the block, nd the block s tested for whether to sort t ths level. ome lossless compresson lgorthms developed recently employ herrchcl mge segmentton for progressve reconstructon. uch lgorthms help us quckly understnd the detled chrcterstcs of the mge. There re two herrchcl mge segmentton methods. One s mult-scle

2 Report Documentton Pge Report Dte 25 Oct 200 Report Type N/A Dtes Covered (from... to) - Ttle nd ubttle ossless Compresson of Medcl Imge by Herrchcl ortng Contrct Number Grnt Number Progrm Element Number Author(s) Proect Number Tsk Number Work Unt Number Performng Orgnzton Nme(s) nd Address(es) Grdute chool of Engneerng Hokkdo Unversty pporo-sh Hokkdo, Jpn ponsorng/montorng Agency Nme(s) nd Address(es) U Army Reserch, Development & tndrdzton Group (UK) PC 802 ox 5 FPO AE Performng Orgnzton Report Number ponsor/montor s Acronym(s) ponsor/montor s Report Number(s) Dstrbuton/Avlblty ttement Approved for publc relese, dstrbuton unlmted upplementry Notes Ppers from 23rd Annul Interntonl Conference of the IEEE Engneerng n Medcne nd oy ocety, October 25-26, 200 held n Istnbul, Turkey. ee lso ADM0035 for entre conference on cd-rom., The orgnl document contns color mges. Abstrct ubect Terms Report Clssfcton unclssfed Clssfcton of Abstrct unclssfed Clssfcton of ths pge unclssfed mtton of Abstrct UU Number of Pges 4

3 Fg.. Reltons mong orgnl block, permutton tble nd sorted block encodng of n mge bsed on wvelet nlyss. Ths method decomposes n mge nto four bnds: HH, H, H,, then reduces the resoluton of the mge [4], [5]. In ths method, chrcterstcs observed n ech bnd re nlyzed nd the overll chrcterstcs re detected s result. Another method s to nlyze the block level chrcterstcs fter subdvdng the mge usng bnry or qud trees [6]. We use the ltter method n order to detect detls of mge structure progressvely. Herefter, we ssume tht ll mges re squre, wth 2 n pxels per sde, nd tht rthms re bse 2. A. Herrchcl sortng As mentoned bove, dgtlly smlr densty ptterns rrely pper n n mge. Further, compred to ordnry 8- bt/pxel photogrphs, 2-bt/pxel medcl mges hve smller lkelhood for ths condton. Ths tendency explns why methods bsed on exct pttern mtchng don't work well for medcl mges. Here we propose nother fundmentl pproch to compressng dgtl mges: We py ttenton to the order of pxel vlues nd not to the pxel vlues themselves, becuse bt depth does not ffect the order of the pxel vlues. Fg. shows the reltonshp mong the orgnl block, the permutton tble nd the sorted block. It s cler tht the sorted block genertes smll predctng code. Our concept, bsed on herrchcl sortng, s to mprove the mge compresson rto by choosng the sze of tble nd usng prtl sortng. We developed tble generton method tht tkes nto ccount only the order of the pxels n block. A-. lock dvson In process smlr to so-clled qud-tree dvson, the mge s dvded nto four non-overlppng squre blocks. The mge to be compressed s represented s squre rry of pxels. For n mge of sze, dvson level n (n = 0,,2,,) s defned. Then, sub-block sze t nd number of blocks N t re defned. A predctve codng method s ppled to ech block nd t produces code of sze c p (n) for dvson level n. At the sme tme, the block s sorted ccordng to permutton tble creted from the pttern of the block. Then the sme predctve coder s ppled to the sorted results. The sze of code generted by ths procedure s c s (n). The dfference of the code szes, c l, s computed by C = C ( n) C ( n). () l p s We select the codng method c for block bsed on the vlue of c l. If c l s greter thn 0, the permutton tble s ppled before predctve codng; otherwse, the predctve coder codes the block drectly. All blocks of re tested usng (), then ech block s tested wth (2) or (3) for whether to do further sub-dvson. y dvdng n mge nto smll sub-blocks, detled chrcterstcs of n mge cn be well understood; however, subdvson of such fne grnulrty wll ncrese the number of blocks to be processed. In the frst step, the entropy of four 0 blocks nd blocks s compred to tht of the code for blocks tht consst of four lrge blocks. The necessty of subdvson s determned by (2). 0 N ) n, ). (2) At subdvson level or hgher, t s not necessry to hve the entropy of ll the sub-mges. Estmtng the entropy of the entre mge t ll dvson levels mght overlook the detls of the mge. Therefore, further subdvson cn be performed loclly by tkng nto ccount only the mge re to be processed. ) 4 + n, + ). (3) The block dvson process ends when / 2 becomes T, where T s the sze permutton tble. A-2. Permutton tble creton We must determne the sze of the permutton tble before strtng herrchcl sortng. et us defne the necessry bts for storng the permutton tble s T bt. When the sze of permutton tble s T, T bt s gven by Tbt = T. As T T ncreses, T bt ncreses rpdly. There re T! dfferent ptterns n the set of permutton tbles of sze T. If we mke T smll, one pttern cn be ppled to mny plces n the mge. However, the result of settng prmeters ths wy s tht complex regons of the mge get dvded nto mny blocks, so mny bts re requred to record the nter-block connectons. Conversely, f T s lrge, the compresson rto of the regon becomes hgh. However, the necessry storge for the permutton tble ncreses nd the lkelhood of pplyng the generted permutton tble to other regons decreses. In order to ncrese the probblty of reusng the permutton tbles, we use fxed-sze permutton tbles for ll dvson levels. Herefter, the word resoluton ndctes the number of segmented regons wthn block tht re formed by qud-tree subdvson or permutton tbles. For exmple, the resoluton of qud-tree block dvson s 4. If

4 the resoluton of the permutton tble s hgher thn tht of qud-tree block dvson, the sortng of overlps tht of +. In the complex regons of n mge, lthough rough sortng s done t, more precse sortng s done on +. We cll ths technque "herrchcl sortng." When the sze of the permutton tble s 2 2, both the resoluton of ths permutton tble nd tht of the qud-tree block dvson re 4. In ths cse, sortng s repeted wthn ech block, nd the sze of the predctng code my become lrge n the complex regons of the mge. Therefore, permutton tble of sze 2 2 s not used wth ths technque. As descrbed bove, f the sze of the permutton tble s 8 8 or greter, multple ppernces of the permutton pttern rrely occurs. Hence, permutton tbles of sze 4 4 re better for our herrchcl sortng.. Codng In herrchcl sortng, n mge s dvded nto two dfferent types of blocks. The block type determnes the encodng method. For one type, only predctve codng s ppled. Ths s clled "codng for smooth regons." For the other type, predctve codng s ppled fter the block s sorted usng permutton tbles. Ths s clled "codng for complex regons." Wth one ddtonl bt used to dentfy the block type, the totl bt count of type bt for n mge becomes: N T. (5) type bt = N = Ech encodng method s explned n the followng sectons. -. Codng for smooth regon Predctve codng must be done t ech dvson level for progressve decodng. When predctve codng strts t the dvson level of, the verge denstes of pxels n ech block t re wrtten to compressed dt strem. et us denote the number of blocks coded by the codng method t s NP, the block t s (m =,2,3, m NP ), nd the n th pxel vlue n s m v (n). The v s the verge m m densty vlue of, so v m v ( n) m = m. (6) The predctve coder encodes ll v generted by (6). Then m the entropy codng s ppled to the result. At further dvson level, the dfference of v nd v + s encoded by the m m predctve coder untl the sze of dvded block equls tht of permutton tble. The predctve coder encodes ll dfferences of the blocks t the dvson level nd the entropy codng s ppled to the generted code set. The results re wrtten n the low order of dvson level. Fg.2. Imge set compresson: shrng permutton-tbles mong mges -2. Codng for complex regon The permutton tbles t ll dvson levels sort ll blocks, nd the predctve coder encodes the pxels n these blocks. The result s sent to the entropy coder. et us denote the frst dvson level of the block-ppled permutton tble s k. If k s hgher thn, we cn use the verge of the prevous dvson level or k-. If the block t k s complex nd the blocks t k+ re smooth, ths method wrtes the verge of the pxels n the k block. If the block t k nd hgher blocks use permutton tbles, the pxels n the block re encoded by usng ll of the permutton tbles generted t the k nd hgher dvson levels. In ths cse, the progressve structure breks down. However, the length tht sequentl decodng requres s only the block sze t k. Fnlly, ll generted codes re combned. The compressed dt conssts of permutton tbles, the tble of block type, nd entropy codes of the smooth nd complex regons. III. IMAGE ET COMPREION The permutton tbles used by our method re of fxed sze. If the mge set hs smlr chrcterstcs, the sme permutton tbles cn be ppled to mny regons of mny other mges. We proposed n mge set compresson method bsed on ths ssumpton. Ths pproch s bsed on herrchcl sortng. Fg. 2 llustrtes the process n whch the permutton tbles of the prevous mge n the set re ppled to the current mge. In Fg. 2, the current mge references only permutton tbles n the prevous two mges, n order to reduce the number of code bts used for referencng. IV. IMPEMENTAION An mge compresson system usng herrchcl sortng s ndependent of the pxel scn nd of the predctve codng methods. In our mplementton, we used the Hlbert curve to scn n mge. We used smple DPCM s the predctve codng method. We showed n Fg. 3 the blocks to whch the permutton tbles were ppled. In our cse, we used 4 4

5 Fg. 4. Compresson rto for medcl mges normlzed by compresson rto by JPEG- (sngle mge compresson) Fg. 5. Compresson rto for medcl mges normlzed by compresson rto by JPEG- (mge set compresson) Fg. 3. Exmples of blocks n whch herrchcl sortng s ppled s the mge set compresson method pxel permutton tbles, wth no lmt on the number of permutton tbles. Fg. 3 shows n exmple of the blocks to whch the herrchcl sortng method ws ppled for X-ry CT mges. In the exmple, we used medcl mge n 2- bt/pxel formt. Fg. 3 s n exmple of our mge set compresson pcked out from the mge sequence n the set of smple mges. Fg. 3 ()(c)(e) were orgnl mge; (b)(d)(f) re permutton tbles generted usng the mge set compresson method. In the complex regons of the mge, permutton tbles were used t severl dvson levels. These regons were hghlghted n (b)(d)(f). It s obvous tht mny more permutton tbles were used for mges (c) nd (e) thn for mge (). Our mge set compresson used the permutton tbles tht were generted for prevous mges. V. REUT AND DICUION Tble shows detls of smple mges tht were used to compre performnce to tht of the stndrd JPEG- method. Fg.4 nd Fg.5 show performnce comprson of the proposed nd stndrd JPEG- compresson methods. As shown n Fg. 4, when the proposed method ws ppled to sngle mge, our method showed poorer performnce thn JPEG- for smller-szed mges ( ). However, t showed superor performnce when the mge resoluton ws greter thn Fg.5 shows the mge set compresson rtos, normlzed by the compresson rtos of JPEG-. As seen n Fg.5, our method outperformed conventonl methods for ll mge szes. Tble. mple mges Pxel sze No. of mges Ctegory 256x MRI mges 52x52 20 X-ry helcl CT mges (chest) 024x024 0 gstrc brum DR mges 2048x CR (chest) mges VI. CONCUION In ths pper, we proposed lossless mge compresson method for medcl mges, bsed on herrchcl sortng. Our method tkes nto ccount both the globl propertes of the mge nd the locl complexty of the pxels. We mplemented the method nd compred performnce to conventonl JPEG- compresson scheme. The results show tht our method cheved compresson rto the sme s or better thn tht of JPEG- when ppled to stndlone mge. Furthermore, s our method s desgned to hndle mge sets produced by medcl nstruments, we confrmed tht t outperforms conventonl methods when ppled to lrge sets of medcl mges. ACKNOWEDGMENT The uthors wsh to thnk Dr. T. Kodm for provdng medcl mges. REFERENCE [] J.. O'Nel Jr., Dfferentl pulse code modulton wth entropy codng, IEEE Trns. Inform, Theory, Vol. IT-2, pp.69-74, Mrch 976. [2] IO/IEC 098-, Dgtl compresson nd codng of contnuous-tone stll mges: Requrements nd gudelnes, Februry 994. [3] M. Wenberger, G. erouss, G. pro, OCO-I: A ow-complexty, Context-sed, ossless Imge Compresson Algorthm, Proc. IEEE Dt Compresson Conference, nowbrd, Uth, Mrch-Aprl 996. [4]. Wng nd M. Goldberg, Progressve mge trnsmsson usng vector quntzton on mges n pyrmd form, IEEE Trns. Commun., Vol. COM-37, No.2, pp , December 989. [5] Amr d nd Wllm A. Perlmn, An mge multresoluton representton for lossless nd lossy compresson, IEEE Trns. Imge Processng, Vol.5, No.9, pp , eptember 996. [6] N. Rngnthn, teve G. Romnuk nd Kmeswr Ro Nmudur, A ossless Imge Compresson Algorthm Usng Vrble lock ze egmentton, IEEE Trns. Imge Processng, Vol.4, No.0, pp , October 995.